Lacunary Statistical Backward Quasi Cauchy Sequences on Asymmetric Spaces

Abstract

We call a sequence (xm) of points in an asymmetric metric space (X, d) lacunary statistically backward quasi Cauchy if limr→∞1hr|{mâIr:d(xm+1,xm)≥ϵ}|=0 for each positive ϵ, where Ir = (kr-1, kr] and k0 = 0, hr = kr-kr-1 → ∞ as r → ∞ and θ = (kr) is an increasing sequence of positive integers and, |A| indicates the cardinality of the set A. © 2025 Author(s).